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Full text of "Analytical Mechanics"

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61.   Simplification of Problems. — The simplest phenomenon in nature is the result of innumerable actions  and reactions.   The consideration of all the factors which contribute to any natural phenomenon would require unlimited analytical power.   Fortunately the factors which enter into dynamical problems are not all of equal importance.   ()ften the influence of one or two predominates so that the rest can be neglected without an appreciable, depart ure from t he act unl problem.  Any one who attempts to solve a physical pro! »lem must recognize this fact and use it to advantage by representing the actual problem by an ideal one which has only the important characteristics of the former.    This was done in the last two chapters in which bodies were t rented as single particles and rigid bodies, and the problems were thereby simplified without changing their character.
The same procedure will be followed in discussing the equilibrium of flexible cords, such as belts, chains, and ropes. These bodies will be represented by an ideal cord of negligible cross-section and of perfect flexibility. The solut ion of the idealized problems gives us a close* enough approximation for practical purposes. If, however, closer approximation is desired smaller factors, such as the effects of t hick ness and imperfect flexibility, may bo taken into account.
62.   Flexibility. —A cord is said to bo perfect It/ Jlcjrthli* if It. offers no resistance to bending; in other words, in a perfectly flexible cord there are no internal forces which net in a direction perpendicular to its length,